2:30 p.m. - 3:30 p.m. Location: GR 2.302
Department of Mathematics and Statistics
University of Nevada, Reno
Self-similar tree representation of coalescent, branching, and time series
Tree graphs provide a close approximation to many natural structures and processes, including river networks, spread of disease or information, transfer of gene characteristics, dynamics of particles with localized interactions, etc. This would sound as a trivial observation if not for the following fact. Despite apparent diversity, a majority of rigorously studied branching structures belong to a two-parametric Tokunaga self-similarity class and exhibit Horton scaling. The Horton scaling is a counterpart of the power-law size distribution of system’s elements. The stronger Tokunaga constraint ensures that different levels of a hierarchy have the same probabilistic structure. I will review the existing results and recent findings on self-similarity for tree representation of branching, coalescent processes and time series. I will also discuss so-called Horton-Smoluchowski differential equations that generalize Smoluchowski description of coalescent phenomena in a tree-oriented framework. This provides a new characterization for the classical Kingman’s coalescent process and suggests a novel view on general coalescence process.
Joint work with Yevgeniy Kovchegov (Oregon State University)
Sponsored by the Department of Mathematical Sciences